Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

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The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

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Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;

public class KarenAndGame {
  public static void main(String[] args) throws IOException {
    BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
    String[] input = in.readLine().split(" ");
    int rows = Integer.parseInt(input[0]);
    int cols = Integer.parseInt(input[1]);
    int[][] a = new int[rows][cols];
    int ROWFIRST = 0;
    int COLFIRST = 1;
    int[][] movesForRow = new int[2][rows];
    int[][] movesForCol = new int[2][cols];
    
    int totalForRow = 0;
    for(int r = 0; r < rows; r++) {
      StringTokenizer t = new StringTokenizer(in.readLine());
      movesForRow[ROWFIRST][r] = Integer.MAX_VALUE;
      for(int c = 0; c < cols; c++) {
        int num = Integer.parseInt(t.nextToken());
        movesForRow[ROWFIRST][r] = Math.min(movesForRow[ROWFIRST][r], num);
        a[r][c] = num;
      }
      totalForRow += movesForRow[ROWFIRST][r];
    }
    for(int c = 0; c < cols; c++)
      totalForRow += movesForCol[ROWFIRST][c] = a[0][c] - movesForRow[ROWFIRST][0];
    
    int totalForCol = 0;
    for(int c = 0; c < cols; c++) {
      movesForCol[COLFIRST][c] = Integer.MAX_VALUE;
      for(int r = 0; r < rows; r++)
        movesForCol[COLFIRST][c] = Math.min(movesForCol[COLFIRST][c], a[r][c]);
      totalForCol += movesForCol[COLFIRST][c];
    }
    for(int r = 0; r < rows; r++)
      totalForCol += movesForRow[COLFIRST][r] = a[r][0] - movesForCol[COLFIRST][0];
    
    boolean works = true;
    for(int r = 0; r < rows && works; r++) {
      for(int c = 0; c < cols && works; c++) {
        if(a[r][c] != movesForRow[ROWFIRST][r] + movesForCol[ROWFIRST][c])
          works = false;
      }
    }
    
    if(!works)
      System.out.println("-1");
    else {
      int rowOrCol = 1;
      if(totalForRow <= totalForCol)
        rowOrCol = 0;
      int totalMoves = 0;
      for(int r = 0; r < rows; r++)
        totalMoves += movesForRow[rowOrCol][r];
      for(int c = 0; c < cols; c++)
        totalMoves += movesForCol[rowOrCol][c];
      System.out.println(totalMoves);
      for(int r = 0; r < rows; r++) {
        for(int i = 0; i < movesForRow[rowOrCol][r]; i++)
          System.out.println("row " + (r+1));
      }
      for(int c = 0; c < cols; c++) {
        for(int i = 0; i < movesForCol[rowOrCol][c]; i++)
          System.out.println("col " + (c+1));
      }
    }
  }
}